The problem is that when in Add or Edit mode (any screen with a submit button), you cannot do what you are attempting to do. Changes to components in Add/Edit mode do not submit back to the google sheet until you click on the Submit button, so filling a search box would not send back to the spreadsheet to perform the filter. In your example where you click a button to link to your search screen, clicking the button takes you to a Detail view. Editable components in Detail view are automatically submitted back to the spreadsheet as they are changed in real time. The reason for this is because, if you are in Detail view, it’s assumed that updates can happen in real time, because you intentionally opened that field up for edit and expect the changes to happen right away. In Add/Edit mode, you always have the option to Cancel, so the submission isn’t committed to the spreadsheet until you are OK with all the changes and click the submit button. Unfortunately, I don’t think there is a simpler solution to doing a search where the data would need to submit back to the spreadsheet. The only other option would be to perform the search prior to clicking on the Add Product button when viewing the shopping list.
As you have it right now, you would have conflicting searches if multiple people are using the app. I assume that is one of the reasons you are trying to bring the search to the list level, but I think it gets complicated since you could return multiple rows of data from the search, so the search results would still need to be in a new sheet and you would still need to link to that new sheet. The flow wouldn’t be any simpler.
Also, right now glide doesn’t allow choice component to be filled differently based on user or different conditions. Whatever is in the sheet is whatever populates in the choice component. You would have to worry each user overwriting any users search results.
This is a bit of rambling, but I just can’t visualize a way to make, what you are attempting, work how you would like it to.